For signals observed in Gaussian noise, we will unveil a new relationship between the
input-output mutual information and the minimum mean-square error (MMSE)
achievable by the optimal estimator of the input. This relationship holds
for arbitrarily distributed scalar and vector signals, as well as for
discrete-time and continuous-time noncausal MMSE estimation (smoothing).

We will also focus on two applications of these information theoretic results:
the mercury/waterfilling formula for power allocation with
arbitrary input constellations; and a universal continuous-time nonlinear filtering
formula that couples the signal-to-noise ratios achievable by smoothing and filtering.

Biography:

Sergio Verdú is a Professor of Electrical Engineering at Princeton University where he teaches and conducts research on information theory in the Information Sciences and Systems Group. He is also affiliated with the Program in Applied and Computational Mathematics.

Sergio Verdú was born in Barcelona, Catalonia, Spain on August 15, 1958. He received the Telecommunications Engineering degree from the Polytechnic University of Barcelona, Barcelona, Spain, in 1980 and the Ph.D. degree in Electrical Engineering from the University of Illinois at Urbana-Champaign in 1984. Conducted at the Coordinated Science Laboratory of the University of Illinois, his doctoral research pioneered the field of Multiuser Detection.
Sergio Verdú was a recipient of a Fulbright Fellowship, the National University Prize of Spain, an IBM Faculty Development Award, the Rheinstein Outstanding Junior Faculty Award of the School of Engineering and Applied Science at Princeton University, a Presidential Young Investigator Award from the National Science Foundation, a Princeton Engineering Council Award for excellence in undergraduate teaching, the 2000 Frederick E. Terman Award from the American Society for Engineering Education, and the IEEE Third Millennium Medal in 2000.